The tasks that unmanned aerial vehicles (UAVs) have taken upon have progressively grown in complexity over the years, alongside with the level of autonomy with which they are carried out. In this work, we present an example of aerial screwing operations with a fully-actuated tilt-rotor platform. Key contributions include a new control framework to automate screwing operations through a robust hole search and in-hole detection algorithm. These are achieved without a-priori knowledge of the exact hole location, and without the use of external tools, such as vision based hole detection or force sensors. Wrench coupling is implemented to account for the platform's kinematic constraints during screwing. The application of a constant contact force and a compliant response to induced disturbances are obtained with the use of admittance control. The full framework is validated with extensive flight experiments that demonstrate the effectiveness of each subsystem, as well as the complete architecture. We also validate the robustness of the detection algorithm against false positives. Within the results we demonstrate the ability to perform the automated task with a 86% success rate over 35 flights, and measured hole search time of 9s (median value).